A. N. Yan | Searcharxiv

arXiv2022

AdS$_3$/AdS$_2$ degression of Fronsdal fields

We analyze the Kaluza-Klein type procedure in AdS$_3$ space called the dimensional degression. The topological theory of the Fronsdal field in AdS$_3$ is reformulated in terms of the fields propagating in AdS$_2$. We find that the Fronsdal field in AdS$_3$ leads to finitely many Kaluza-Klein modes. Namely, the obtained spectrum is the massive Klein-Gordon and Proca fields in AdS$_2$. The result is derived by using the specific mode expansion, the gauge fixing, and 2-dimensional Schouten identities.

hep-th↗

arXiv2021

AdS$_3$/AdS$_2$ degression of massless particles

We study a 3d/2d dimensional degression which is a Kaluza-Klein type mechanism in AdS$_3$ space foliated into AdS$_2$ hypersurfaces. It is shown that an AdS$_3$ massless particle of spin $s=1,2,...,\infty$ degresses into a couple of AdS$_2$ particles of equal energies $E=s$. Note that the Kaluza-Klein spectra in higher dimensions are always infinite. To formulate the AdS$_3$/AdS$_2$ degression we consider branching rules for AdS$_3$ isometry algebra o$(2,2)$ representations decomposed with respect to AdS$_2$ isometry algebra o$(1,2)$. We find that a given o$(2,2)$ higher-spin representation lying on the unitary bound (i.e. massless) decomposes into two equal o$(1,2)$ modules. In the field-theoretical terms, this phenomenon is demonstrated for spin-2 and spin-3 free massless fields. The truncation to a finite spectrum can be seen by using particular mode expansions, (partial) diagonalizations, and identities specific to two dimensions.

hep-th↗